But there is increasing concern that organized crime is getting in the "back door" -- through Local 54 of the Hotel, Restaurant, and Bartenders International Union, a member of the AFL-CIO.

In fact, law-enforcement officials investigating the 7,600- member local told the Monitor in extensive interviews that they are certain mob elements control it and that labor racketeering is virtually "inevitable."

One such official, who requested his name not be used, stressed that to date the union had not, according to informants, "engaged in any illegal activity" by "selling labor peace" or through other usual racketeering practices.

At the same time, both the Atlantic County prosecutor's office and the New Jersey State Police special casino investigation unit are actively probing the activities of the union with the hope that this action can help prevent wrongdoing.

Local 54 has become one of the largest unions in New Jersey due to the growth of casino gambling. Sources say its membership may eventually climb to 200,000 if all the planned casinos are built and opened here. Law-enforcement officials say they believe that the local is heavily influenced -- some say flatly "controlled" -- by elements of organized crime because of situations like the following:

* Robert J. Lumio, secretary-treasurer of the union, is identified as a close associate of Nicodemeo (Little Nick) Scarfo. Law-enforcement agents watching organized crime allege Mr. Scarfo became Atlantic City's chief "crime boss" following the March 1980 shooting death of Angelo Bruno, reputed Philadelphia and south Jersey organized crime leader. Mr. Lumio was convicted seven years ago in Philadelphia of "conspiracy to transport gaming information."

* Frank Materio, a former Local 54 organizer, is also identified as a close associate of Scarfo. Two years ago, Mr. Materio put up his home as collateral for a bond used to free Scarfo and two co-defendants from jail after they were charged in Philadelphia with the murder of a cement contractor. The three men were subsequently acquitted last October. In 1963, Scarfo was convicted on charges of "voluntary manslaughter" and served a jail sentence.

* Lillian Gerace, the mother of Local 54 president Frank Gerace, provided $20 ,000 of the $75,000 bail used to free Scarfo and his co-defendants after a Philadelphia grand jury indicted them for murder in 1979. Mrs. Gerace lives in the same apartment house in an Italian neighborhood of Atlantic City known as "Ducktown" that her son, Frank, and Scarfo and Lumio do.

For his part, Mr. Gerace told the Monitor that allegations about the local's links to organized crime have been drummed up by "anti-gaming" forces.

Gerace also defended other union officials said to be close associates of organized crime figures.When told that Lumio was formerly a bartender at the My Way Lounge, which law- enforcement officials say was frequently by mob members, Gerace replied. "There were 40 other people who worked in the My Way Lounge." He also said he found nothing wrong in his mother contributing to the bail of a friend, even if that friend was alleged mobster Scarfo.

One top law-enforcement official countered that both current and former union leaders "are unusually friendly with people who have been identified as organized crime figures. It is because of their relationship that one has to come to the conclusion that the union is controlled by organized crime."

However, proving these allegations with the aid of informants and other means will take time, this official cautioned.

Investigators hope the continued association of a number of union officials with mob figures will aid their probe. They say that long after two union officials were appointed they often were seen with Scarfo and other reputed mob figures.

"The union has the potential of getting in and controlling the casinos," says one investigator.

Yet investigators hope that their ongoing probe may have "some deterrent effect" on the union's control of casinos. Even though many potential investors have backed off on plans to build casinos here, three more are expected to open within the next several months. These will be a major enticement for organized crime takeover attempts, according to the Atlantic County prosecutor's office.

The power of the New Jersey Division of Gaming Enforcement over the union is described by law officials as "minimal" because the regulation of unions is primarily seen as a federal responsibility. The division does have the power to prohibit casino employees from paying dues to the union if the union engages in racketeering or other wrongdoing. But official say this power should only be considered a "fi rst step" toward greater state control over the union.